Infinitely long cylinder of radius R is made of an unusual exotic material with refractive index -1 (figure). The cylinder is placed between two planes whose normals are along the y-direction. The centre of the cylinder O lies along they-axis.A narrow laser beam is directed along the y-direction from the lower plate. The laser source is at a horizontal distance x from the diameter in the y direction. Find the range of x such that light emitted from the lower plane does not reach the upper plane.
This is a long answer type question as classified in NCERT Exemplar
Since the material is of refractive index , is negative and is positive
| |= | |=| |
Explanation- since the material is of refractive index , is negative and is positive
| |= | |=| |
The total deviation of the outcoming ray from the incoming ray is 4 rays shall not receive if
<4 <
<4 <
sin =x/R
-1x/R<
Light emitted from the source shall not reach the receiving plate under
...more
This is a long answer type question as classified in NCERT Exemplar
Since the material is of refractive index , is negative and is positive
| |= | |=| |
Explanation- since the material is of refractive index , is negative and is positive
| |= | |=| |
The total deviation of the outcoming ray from the incoming ray is 4 rays shall not receive if
<4 <
<4 <
sin =x/R
-1x/R<
Light emitted from the source shall not reach the receiving plate under this condition.
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<p><span data-teams="true">This is a long answer type question as classified in NCERT Exemplar</span></p><p>Since the material is of refractive index <math><mi>μ</mi><mo>-</mo><mn>1</mn></math> , <math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mi>r</mi></mrow></mrow></msub></math> is negative and <math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mi>r</mi></mrow></mrow></msub></math> is positive</p><p>| <math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mi>t</mi></mrow></mrow></msub></math> |= | <math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mi>r</mi></mrow></mrow></msub></math> |=| <math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mi>r</mi></mrow></mrow></msub></math> |</p><p>Explanation- since the material is of refractive index <math><mi>μ</mi><mo>-</mo><mn>1</mn></math> , <math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mi>r</mi></mrow></mrow></msub></math> is negative and <math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mi>r</mi></mrow></mrow></msub></math> is positive</p><p>| <math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mi>t</mi></mrow></mrow></msub></math> |= | <math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mi>r</mi></mrow></mrow></msub></math> |=| <math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mi>r</mi></mrow></mrow></msub></math> |</p><p>The total deviation of the outcoming ray from the incoming ray is 4 <math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mi>t</mi></mrow></mrow></msub></math> rays shall not receive if</p><p><math><mfrac><mrow><mrow><mi>π</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac></math> <4 <math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mi>t</mi></mrow></mrow></msub></math> < <math><mfrac><mrow><mrow><mn>3</mn><mi>π</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac></math></p><p><math><mi>o</mi><mi>n</mi><mi></mi><mi>s</mi><mi>o</mi><mi>l</mi><mi>v</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi></mi></math> <math><mfrac><mrow><mrow><mi>π</mi></mrow></mrow><mrow><mrow><mn>8</mn></mrow></mrow></mfrac></math> <4 <math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mi>t</mi></mrow></mrow></msub></math> < <math><mfrac><mrow><mrow><mn>3</mn><mi>π</mi></mrow></mrow><mrow><mrow><mn>8</mn></mrow></mrow></mfrac></math></p><p>sin <math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mi>t</mi></mrow></mrow></msub></math> =x/R</p><div><div><p><span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>8</mn> </mrow> </mrow> </mfrac> </math> </span><sin<sup>-1x/R<<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>3</mn> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>8</mn> </mrow> </mrow> </mfrac> </math> </span></sin</sup></p></div><div><p><span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>8</mn> </mrow> </mrow> </mfrac> </math> </span> <math> <mfrac> <mrow> <mrow> <mn>3</mn> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>8</mn> </mrow> </mrow> </mfrac> </math></p><p>Light emitted from the source shall not reach the receiving plate under this condition.</p></div></div>
A total refractive prism is also known as a total internal reflection prism. It is an optical prism that is designed for reflecting 100% of the incident light. This happens since this prism uses the principle of total internal reflection. These prisms are oriented and shaped in a specific way so that the light that enters at a specific angle is completely reflected inside the prism. A right-angle prism, porro prism, dove prism and roof prism are some of the examples of total reflective prism.
Total deviation in a prism is the total angle by which the light ray gets bent as it passes through the prism. It is an angle between incident ray and emergent ray of the prism. When a light enters the prism, it will bend towards the normal. After that, it will travel through the prism and bend away from the normal as it exits. Total deviation is the sum of these two from which the apex angle is subtracted.
The formula for total deviation for a prism is as follows:
There are different types of glasses that are used in optical instruments, including the following:
Crown glass (K): This glass is used in eyeglasses, microscopes and cameras. It is used in prisms and windows in optical systems. Crown glass has a low refractive index, low dispersion and excellent transparency in visible spectrum.
Flint Glass (F): This glass, when combined with crown glass, can correct chromatic aberration in lenses. They are also used in prisms for spectroscopy.
Extra-low dispersion glass: These glasses are used in premium optics that are also used for making high-quality camera lenses, telescopes and binoculars.
Optical instruments can have some of the following defects that may impact their performance, which have arisen due to design limitations, manufacturing and physical properties of light:
Chromatic Aberration: This defect occurs because of the different wavelengths of light that refract at slightly different angles when they pass through the lens. It causes them to focus on different points.
Spherical Aberration: This happens because light rays pass through the edges of spherical lens or reflect off spherical mirror focus at different point than rays that pass through the center.
Astigmatism: This type of defect occurs due to the uneven cu
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Optical instruments can have some of the following defects that may impact their performance, which have arisen due to design limitations, manufacturing and physical properties of light:
Chromatic Aberration: This defect occurs because of the different wavelengths of light that refract at slightly different angles when they pass through the lens. It causes them to focus on different points.
Spherical Aberration: This happens because light rays pass through the edges of spherical lens or reflect off spherical mirror focus at different point than rays that pass through the center.
Astigmatism: This type of defect occurs due to the uneven curvature of lenses or mirrors, which causes light to focus differently in horizontal and vertical planes.
Field Curvature: One of the defects in optical instruments is field curvature, which occurs due to flat image sensors and film that cannot perfectly match the curved focal plane of a lens.
Yes, optical instruments are used in modern medicine for many purposes including surgery, monitoring, research and diagnosis. Let us take a look at each one by one:
Many optical instruments are used for visualizing internal structures for diagnosis of a disease and its monitoring. These include Ophthalmoscope, Endoscope, Colposcope and Dermatoscope.
Optical instruments are also used for precision and minimally invasive surgeries, including Laparoscope, Arthroscope and Surgical Microscopes.
Lasers are used for cutting, therapy and coagulation since they have precision and minimal invasiveness. CO? Laser, Excimer Laser and Fiber Optic
...more
Yes, optical instruments are used in modern medicine for many purposes including surgery, monitoring, research and diagnosis. Let us take a look at each one by one:
Many optical instruments are used for visualizing internal structures for diagnosis of a disease and its monitoring. These include Ophthalmoscope, Endoscope, Colposcope and Dermatoscope.
Optical instruments are also used for precision and minimally invasive surgeries, including Laparoscope, Arthroscope and Surgical Microscopes.
Lasers are used for cutting, therapy and coagulation since they have precision and minimal invasiveness. CO? Laser, Excimer Laser and Fiber Optic Lasers are some of the optical instruments.
Optical instruments also help in monitoring vital signs in the body as well as for analysing biological samples. Pulse Oximeter, Spectrophotometer and Optical Coherence Tomography (OCT) are some of the optical instruments.
For cellular-level analysis and medical research, optical instruments like the Confocal Microscope and Fluorescence Microscope are used.
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